The enigma of nonholonomic constraints

The problems associated with the modification of Hamilton’s principle to cover nonholonomic constraints by the application of the multiplier theorem of variational calculus are discussed. The reason for the problems is subtle and is discussed, together with the reason why the proper account of nonholonomic constraints is outside the scope of Hamilton’s variational principle. However, linear velocity constraints remain within the scope of D’Alembert’s principle. A careful and comprehensive analysis facilitates the resolution of the puzzling features of nonholonomic constraints.